Plants show up in the Plant Schedule and on the plan drawing, but if you need to alter or edit them, you attempted to open the Plant Manager and check the Placed box. Only a few of the plants appear in the list for you to edit, as opposed to all plants in the schedule.
Once you place plants into a drawing, they are marked as having been Placed. As the system does not know whether you have subsequently deleted those plants, or abandoned that .dwg file entirely, it does not unmark their Placed status.
At a later date, the Plant Schedule tool may indeed update the Placed/Unplaced status of plants.